Science: If you put paint on the end of a tuning fork and let it dry, and had an identical tuning fork that did not have paint on it, if you sounded each tuning fork, they would sound very slightly different. If you used sealant instead of paint, the tuning fork would still sound slightly different. If you put anything onto the wood of a blade, it will have some impact because now it is not just the wood. That includes glue, rubber, anything. But we buy the blades we do to put the glue and rubbers on. So, in a way the question is besides the point.
It is also worth knowing that, if a blade maker makes a blade with the same wood plies, say he has pieces for each ply that are enough to make two blades and he laminates the plies for one blade with one or a few different kinds of glue, and on the other blade he laminates the wood plies with different kinds of glue: those two blades even though the wood came from the same cut, those two blades will feel different.
Sealing a blade:
So, If you add sealant to a blade, even a thin layer, it will have an effect, even if a very small effect, on how the blade feels: why is this scientifically the case? Anything you put on the wood will change how it feels.. The actual questions that are important are:
1) Would you notice? If not, then it would not matter? Most people would not be able to tell the difference. Some would but it still just would not matter much.
2) Would the way the sealant impacts the blade's feeling make the blade feel better to you or worse? This is a personal choice. For some, the sealant would actually make the blade feel better. For some, it would do the opposite. Again, it is a personal choice.
Seal your blades if you want to, don't if you do not. Also, please note, Stiga makes a whole series of blades with what they call an NCT coating. It is basically a fairly thick, fancy layer of sealant. Those blades feel amazing to me.

Yes, Stiga knows how to add that layer in a way that makes the blade feel really crisp and have a real nice snap to it.
There is no question that using water based glue on your blade face will cause the top ply of your blade to absorb some of the water. If you glue regularly, it that will cause the blade to feel duller over the course of 5-10 changes of rubber. If that issue is more important to you than the change of feeling you get from applying sealant, then you would want to seal the blade. If you don't care about the water from the glue but do care about the change in feeling from adding the sealant, then you would not want to seal. Honestly, either choice is fine. Either has advantages and disadvantages. It is not a big deal either way. If you are using a blade with a harder top ply like Koto, the benefits of sealing are less useful than if your blade has a softer more delicate top ply like Limba.
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Sealing the handle:
It is a personal choice here too. I have used blades with sealed handles. I hate how it feels. Lazer is right: it will keep the handle looking better; the handle will stay looking fresh and new exponentially longer. For some that is good. I like my blades and handles looking beat up and old like they have been used, been through the wars and have the dirt, the dings, the sweat stains, the battle scars to show for it. But some people like their blades to stay looking neat and clean. Either is fine.
For me, when there is sealant on the handle, I hate how the handle feels and, yes, it feels slippery to me. And no, I don't like grip tape. But plenty of people do like grip tape.
Most well made TT blades, the handle, the wood of the handle is very good at absorbing sweat and keeping your hand dryer when you are playing. I like that. When the blade's handle is sealed it will not absorb your sweat. But definitely will stay looking good for longer. So, again, it is a personal choice. If you like how a handle feels with sealant on it, and you want to protect the wood from water, it will be useful, and it will keep the handle looking very close to how it looked new. And the people who don't like the feel of sealant on the handle, those people should not use sealant.
So, again the real issue with sealing the handle is about personal choice.